Sample space is defined as the set or collection of all possible outcomes of a probability experiment.
Ex. How many elements are in the sample space of rolling one dice?
Answer: There are 6 sides on the dice so the sample space is {1,2,3,4,5,6}
Ex. How many elements are in the sample space of tossing 3 nickels?
Answer: All the possible outcomes are as listed: {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}
Since the sample space is all the possible outcomes you can list all the combines as above, or you can multiply 2*2*2. For each penny there is two possible outcomes, and you mulitply that by the number of pennies being tossed.
Ex. There are 3 entry doors and 2 staircases in your house. How many ways are there to enter the house and go to the second floor?
Answer: So since there are 3 entry doors and 2 staircases you multiply 3*2 and get 6. So you know there are 6 possilbe ways to enter the house and get to the second floor. The following is the sample space: {Door1-Stair1, Door1-Stair2, Door2-Stair1, Door2-Stair2, Door3-Stair1, Door3-Stair2}
Ex. How many elements are in the sample space of rolling one dice?
Answer: There are 6 sides on the dice so the sample space is {1,2,3,4,5,6}
Ex. How many elements are in the sample space of tossing 3 nickels?
Answer: All the possible outcomes are as listed: {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}
Since the sample space is all the possible outcomes you can list all the combines as above, or you can multiply 2*2*2. For each penny there is two possible outcomes, and you mulitply that by the number of pennies being tossed.
Ex. There are 3 entry doors and 2 staircases in your house. How many ways are there to enter the house and go to the second floor?
Answer: So since there are 3 entry doors and 2 staircases you multiply 3*2 and get 6. So you know there are 6 possilbe ways to enter the house and get to the second floor. The following is the sample space: {Door1-Stair1, Door1-Stair2, Door2-Stair1, Door2-Stair2, Door3-Stair1, Door3-Stair2}
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